Enter the equations of the asymptotes for the function

the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote

solve x - 7 = 0 ⇒ x = 7 is the asymptote

horizontal asymptotes occur as

[tex]lim( x → ± ∞), f(x) → c ( where c is a constant )

divide terms on numerator/ denominator by x

f(x) = (3/x/x/x -7/x ) + 2

as x → ± ∞, f(x) → 0 / 1 - 0 + 2 = 2

y = 2 is the asymptote

tramserran tramserran · Answer 2 · 2018-12-29T10:08:40+01:00

Answer: Vertical asymptote is x = 7

Horizontal asymptote is y = 2

Step-by-step explanation:

The vertical asymptote is the restriction on the domain (x-value). Since the denominator cannot be zero ⇒ x - 7 ≠ 0 ⇒ x ≠ 7 so the vertical asymptote is at x = 7.

The horizontal asymptote (H.A.) is the restriction on the range (y-value). There are three rules that determine the horizontal value which compare the degree of the numerator (n) with the degree of the denominator (m):

If n > m , then there is no H.A. (use long division to find the slant asymptote)
If n = m , then the H.A. is the coefficient of n ÷ coefficient of m
If n < m, then the H.A. is y = 0

In the given problem, n = 0 and m = 1 ⇒ n < m ⇒ H.A. is y = 0

Since there is a vertical shift of +2 units, the H.A. is y = 0 + 2 ⇒ y = 2